This type of mass flow meter for flowing media, which operates according to the Coriolis principle, is known for example from DE 196 20 079 C2. This document describes mass flow meters of which the Coriolis measuring tube is embodied as a straight tube and also those with a curved, especially loop-shaped Coriolis measuring tube. A distinction is also made between mass flow meters which only feature one Coriolis measuring tube and those with two Coriolis measuring tubes. In the embodiments with two Coriolis measurement tubes, these can be positioned in series or parallel as regards flow technology. With mass flow meters with two straight or curved measuring tubes these tubes are mostly identically embodied in pairs and are arranged and made to oscillate so that they oscillate against one another. The position of the mass center point remains constant in this case and forces arising are compensated for. The positive consequence of this is that the oscillating system has no effect externally. No oscillations are therefore introduced into the pipework system into which such a mass flow meter is built and conversely oscillations in the pipework system do not influence the measurement result if the mass flow meter is of an appropriate design.